Londýnska matematická spoločnosť: študijné texty Séria

Focusing on the classical aspects of Banach space theory, this short course covers three key topics: Schauder bases, Lp spaces, and C(K) spaces. It highlights the postwar revival of the field led by notable mathematicians such as James and Lindenstrauss, showcasing their impactful results. A foundational knowledge of functional analysis and some exposure to abstract measure theory is required, along with a basic understanding of topology, although an appendix is provided for necessary topological concepts.

The book focuses on modern set theory techniques that are particularly relevant to various fields of pure mathematics. It explores how these methods can be applied to enhance understanding and problem-solving across different mathematical disciplines, making it a valuable resource for mathematicians seeking to deepen their knowledge and skills in set theory and its applications.

Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

This text is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before using it to study a range of randomized algorithms with important applications in optimization and other problems in computing. The book will appeal not only to mathematicians, but to students of computer science who will discover much useful material. This clear and concise introduction to the subject has numerous exercises that will help students to deepen their understanding.

The book provides a comprehensive overview of computational techniques for solving diophantine equations, focusing on the mathematical concepts and algorithms involved. It explores various methods, offering insights into their applications and effectiveness in tackling these equations. The text is designed for both researchers and students, aiming to enhance understanding of this complex area in number theory.

The book is a self-contained introduction to the results and computational methods in classical invariant theory. It relies on minimal mathematical prerequisites, and can be read by advanced undergraduate or graduate students. A variety of innovations will also make the book of interest to specialists and researchers.